Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

BACKGROUND

In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions.

METHODS

Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 "High-dimensional data" of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD.

RESULTS

The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided.

CONCLUSIONS

This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses.

Transforming RNA-Seq data to improve the performance of prognostic gene signatures

Gene expression measurements have successfully been used for building prognostic signatures, i.e for identifying a short list of important genes that can predict patient outcome. Mostly microarray measurements have been considered, and there is little advice available for building multivariable risk prediction models from RNA-Seq data. We specifically consider penalized regression techniques, such as the lasso and componentwise boosting, which can simultaneously consider all measurements and provide both, multivariable regression models for prediction and automated variable selection. However, they might be affected by the typical skewness, mean-variance-dependency or extreme values of RNA-Seq covariates and therefore could benefit from transformations of the latter. In an analytical part, we highlight preferential selection of covariates with large variances, which is problematic due to the mean-variance dependency of RNA-Seq data. In a simulation study, we compare different transformations of RNA-Seq data for potentially improving detection of important genes. Specifically, we consider standardization, the log transformation, a variance-stabilizing transformation, the Box-Cox transformation, and rank-based transformations. In addition, the prediction performance for real data from patients with kidney cancer and acute myeloid leukemia is considered. We show that signature size, identification performance, and prediction performance critically depend on the choice of a suitable transformation. Rank-based transformations perform well in all scenarios and can even outperform complex variance-stabilizing approaches. Generally, the results illustrate that the distribution and potential transformations of RNA-Seq data need to be considered as a critical step when building risk prediction models by penalized regression techniques.

Stability investigations of multivariable regression models derived from low- and high-dimensional data

Multivariable regression models can link a potentially large number of variables to various kinds of outcomes, such as continuous, binary, or time-to-event endpoints. Selection of important variables and selection of the functional form for continuous covariates are key parts of building such models but are notoriously difficult due to several reasons. Caused by multicollinearity between predictors and a limited amount of information in the data, (in)stability can be a serious issue of models selected. For applications with a moderate number of variables, resampling-based techniques have been developed for diagnosing and improving multivariable regression models. Deriving models for high-dimensional molecular data has led to the need for adapting these techniques to settings where the number of variables is much larger than the number of observations. Three studies with a time-to-event outcome, of which one has high-dimensional data, are used to illustrate several techniques. Investigations at the covariate level and at the predictor level are seen to provide considerable insight into model stability and performance. While some areas are indicated where resampling techniques for model building still need further refinement, our case studies illustrate that these techniques can already be recommended for wider use.